Question

Is there a relationship between total team salary and the performance of teams in the National Football League (NFL)? For the 2012-2013 season, a linear model predicting Wins (out of 16 regular season games) from the total team Salary ($M) for the 32 teams in the league is:
Wins — —16.32 + 0.219 Salary
a) What is the explanatory variable?
b) What is the response variable?
c) What does the slope mean in this context?
d) What does the y-intercept mean in this context? Is it meaningful?
f) If one team spends $10 million more than another on salary, how many more games on average would you predict them to win?
e) If a team spent $120 million on salaries and won 8 games, would they have done better or worse than predicted?
f) What would the residual of the team in part f be?
g) The residual standard deviation is 2.78 games. What does that tell you about the likely practical use of this model for predicting wins?